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Pseudo-holomorphic curves on almost complex manifolds have been much more intensely studied than their "dual" objects, the plurisubharmonic functions. These functions are defined classically by requiring that the restriction to each…

In this article we prove in the main theorem that, there is a bijection between the isomorphism classes of a certain type of real hyperplane arrangements on the one hand, and the antipodal pairs of convex cones of an associated…

We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…

This work is dedicated to the development of the theory of Fourier hyperfunctions in one variable with values in a complex non-necessarily metrisable locally convex Hausdorff space $E$. Moreover, necessary and sufficient conditions are…

We have proved that homeomorphisms of domains of Euclidean space, inverse of which distort the modulus of families of curves by Poletskii type, have a continuous extension to isolated boundary point.

By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second…

The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such…

Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…

Many geometric learning problems require invariants on heterogeneous product spaces, i.e., products of distinct spaces carrying different group actions, where standard techniques do not directly apply. We show that, when a group $G$ acts…

In this paper, we consider an infinite derivative scalar field action with infinite derivative kinetic and interaction terms. We establish that the theory is unitary if the correlation functions are formulated in Euclidean space and then…

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a…

Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…

Let $V$ be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on $V$, $\CL f = \sum_{x \in V} f(x)\rho(x)$, where $\rho$ is a nonzero function on $V$. Polynomial subspaces that…

Consider a real diagonal deterministic matrix $X_n$ of size $n$ with spectral measure converging to a compactly supported probability measure. We perturb this matrix by adding a random finite rank matrix, with delocalized eigenvectors. We…

We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…

For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…

The paper is devoted to a comprehensive second-order study of a remarkable class of convex extended-real-valued functions that is highly important in many aspects of nonlinear and variational analysis, specifically those related to…

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Moebius group of the projective line. Since the general proof is very simple but not…